The Frank copula
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The Frank copula is a copula that is sometimes used
in the modelling of codependency. It is an Archimedean copula,
and exchangeable.
Copula name
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Frank copula
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Common notation
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![](I/FrankCopula_files/image001.png)
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Parameters
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![](I/FrankCopula_files/image002.png)
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Domain
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![](I/FrankCopula_files/image003.png)
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Copula
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![](I/FrankCopula_files/image004.png)
Or if we use the limit which
the independence
copula
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Kendall’s rank
correlation coefficient (for bivariate case)
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![](I/FrankCopula_files/image007.png)
where is
the Debye function defined as:
![](I/FrankCopula_files/image009.png)
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Coefficient of upper
tail dependence, ![](I/FrankCopula_files/image010.png)
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![](I/FrankCopula_files/image011.png)
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Coefficient of lower
tail dependence, ![](I/FrankCopula_files/image012.png)
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![](I/FrankCopula_files/image011.png)
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Archimedean generator
function, ![](I/FrankCopula_files/image013.png)
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![](I/FrankCopula_files/image014.png)
Or if we use the limit which
is taken as ![](I/FrankCopula_files/image016.png)
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Other comments
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If we obtain the independence copula.
The Frank copula (like the Clayton copula) is a comprehensive
copula in that it interpolates between a lower limit of the countermonotonicity
copula ( ) and an upper limit of the comonotonicity
copula ( ).
|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “Frank Copula”.
For details of other supported probability distributions see here.
NAVIGATION LINKS
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